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Morse Structures on Open Books

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HTL - Homology theories in low dimensional topology

Every contact 3-manifold is locally contactomorphic to the standard contact R3, but this fact does not necessarily produce large charts that cover the manifold efficiently. I'll describe joint work with Dave Gay and more recently, Dan Mathews, which uses an open  book decomposition of a contact manifold to produce a particularly efficient collection of such contactomorphisms, together with simple combinatorial data describing how to reconstruct the contact 3-manifold from these charts.   We use this construction to define  front projections for Legendrian knots and links in arbitrary contact 3-manifolds, generalising existing constructions of front projections for Legendrian knots in S3 and universally tight lens spaces.



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